Despite unsealing the Gloomy Cavern during the Fireworks Festival main quest, unsealing the other mysterious cavern doors in will require you to find more sets of Launch Tubes to activate.
This isn't so simple, and the maps provided will still take some puzzling out to understand exactly where they're pointing, but it's worth the work for the treasures that lie inside. Your first task will be to find all three other caverns on the Firework Isle.
These cavern doors, seen first in "" main event quest, require three Launch Tubes to be activated using the Firey Glow ability outfit to be unsealed. Each gate has a stone map in front of it, marking the locations of the other caverns on the island and the locations for the Launch Tubes that must be activated before they open. Find all three for each door to reveal the treasure that lies inside.
There are four caverns to be found on the Firework Isle, and the first one is revealed in the main event quest, as mentioned above.
The other three can be found by looking at the stone map in front of the Gloomy Cavern or simply exploring the Isle. One is found directly north of the Songbreeze Highland Hillside Warp Spire and is by far the simplest to find.